The city-state, with a population of only around 5.5 million, already has three mobile-service operators, all of which have some government-linked ownership. And there aren't a lot of residents who haven't already picked a carrier: The mobile penetration rate is hovering around 150 percent, meaning many people have more than one device, according to Ryan Tay, senior research manager of Telecoms at IDC Asia Pacific.

But Malcolm Rodrigues, founder and chief executive officer of internet service provider MyRepublic, believes there's room for a fourth telco in Singapore.

"There's a whole other climate for data, as we expect the Singapore mobility market to grow from 8 million to 9 million over the next year, and the demand for Internet of Things (IOT) will also see over 50 million devices requiring connectivity in the next five years," Rodrigues told CNBC.

"Existing operators are not ready to support it," said Rodrigues, who is also a former senior executive at StarHub, one of Singapore's three telecommunication companies.

Rodrigues isn't alone in thinking another company can eke out a share of the tight market.

IDC Asia Pacific's Tay thinks there's definitely room for a fourth telco in Singapore, "considering the growing trend of people owning more than one mobile device, driven by the shift towards a mobile workforce and consumerization."

The government is on board with adding another competitor as it's looking ahead to keeping up with technology advances. The Infocomm Development Authority of Singapore (IDA) told CNBC that "with consumers' increasing demand for mobile broadband service, new technology and service developments in the industry (e.g. emergence of 'Machine-to-Machine' communications), there may be new business opportunities and market segments for new players."

MyRepublic is aiming to win 9 percent of the Singapore mobile market within five years, a goal its CEO calls "pretty conservative." The company is already offering a home broadband service in Singapore, with 50,000 subscribers.

But it's not clear how much of the pie is up for grabs. Currently, IDC estimates SingTel has around 50 percent of Singapore's mobile subscribers, while StarHub has 27 percent and M1 has 23 percent.

Those three aren't twiddling their thumbs while waiting for competition to arrive.

In early March, Singtel, StarHub and M1 announced they slashed their post-paid users' prices for add-on mobile data. In local media, it was widely reported as a "mobile price war" ahead of potential entrants.

"The competitive pricing for add-on data and upsize option could be a ploy to counter MyRepublic's data-only plans," said Jonathan Koh, analyst at UOB Kay Hain, in a March 17 note. "Incumbents Singtel, M1 and StarHub are signaling their determination to do "whatever it takes" to defend their market shares."

Additionally, any new player is likely to start on the back foot.

"We believe any potential new player is unlikely to have a competitive advantage on cost structure to build a viable business plan," said analysts at Deutsche Bank in a March 16 note.

The new player would also be up against integrated players StarHub and Singtel offering multiple services, such as broadband internet and cable television, which allow them to employ bundling strategies, said Deutsche Bank.

But MyRepublic's Rodrigues is looking at M1's customer base, saying it's "probably most at risk because of their limited service offerings," which are primarily mobile service and home broadband.

M1 "will be the most aggressive in the market as they try to retain their customers," said Rodrigues.

MyRepublic is planning to aim for the market fringes: both the lower end of the mobile market, or pre-paid users, and the highest end, Rodrigues said. The company has already announced its two planned pricing plans: The first with 2 gigabytes of data at 4.5G network speeds for S$8 ($5.80) monthly with additional data charges at S$8/GB and the second for an unlimited data-usage mobile plan costing S$80 ($58.40) per month.

That would make MyRepublic the first telco in Singapore to offer unlimited mobile data usage plans.

The lowest data usage SIM-only mobile plans offered by StarHub and Singtel are 3GB at S$21.45 ($15.65) and S$20 ($14.60) respectively, compared to MyRepublic's 3GB mobile plan for S$16. On the higher end of the market, it would cost S$110 ($80.30) for a StarHub 12GB mobile plan, compared to MyRepublic's unlimited data usage plan capped at S$80 ($58.40).

Rodrigues, who is Canadian, told CNBC that he's already pleased with the registration of interest on MyRepublic's website. In under a week, about 15,000 people had registered their interest, 80 percent of which were interested in the unlimited data mobile plan.

But first, MyRepublic has other hurdles to jump: The spectrum auction likely won't be held until the third quarter of this year, and it's not the only one throwing its hat into the ring.

Wireless software services provider Consistel's OMGtel has also announced its interest in a sliver of Singapore's market.